Theoretical and Experimental Approaches to Institutional Design: Applications to IPO Auctions and Weighted Voting Games - Zhang, Ping (2006)
Multiple solutions often exist in both non-cooperative and cooperative games. In this thesis we use game theoretical arguments and experiments to examine multiplicity in two different areas, namely uniform price auctions and weighted voting games. In the second chapter we develop a theoretical model of IPO auctions and show that when demand is discrete the tacit collusion equilibrium is obtained under a stricter condition than in the continuous format. There also exists a continuum of equilibria where investors with a higher expected valuation bid more aggressively, and as a result the market price increases with market value. The tacit collusion equilibrium is in fact an extreme case of this set. Bertrand competition, i.e, submitting a flat demand function, does not form an equilibrium in this game. We then test our equilibrium predictions and compare the performances of uniform price auctions with fixed price offerings using laboratory experiments. In the uniform treatment, there is no evidence that the tacit collusion equilibrium has been achieved. On the contrary, subjects with higher expected value bid more aggressively. Their behaviour is close to an equilibrium derived where all players participate. The resulting market prices are significantly higher than the market value of an investor with a low value signal. As a consequence, in our experiment uniform price auctions are superior to fixed price offerings in terms of revenue raising. In chapter four we move to weighted voting games. Power indices predict that enlargement of the voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the existing voters may actually gain, a phenomenon known as the paradox of new members. We test for this effect using laboratory experiments. We find empirical support for the paradox of new members. Our results also allow an assessment of the predictive performance of standard power indices.